# How to Find the Magnitude of the Vector

By Oxana Fox
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A vector is a geometric object that has both length and direction. Vectors play an important role in science as they can represent physical quantities, for example, the velocity of a plane moving at 600 mph in a northeasterly direction. Each vector has coordinates or components, such as “X” and “Y.” A vector also has magnitude, or length, representing the raw "amount" of a measurement. For a velocity vector, for example, the magnitude represents speed. The calculation of the magnitude is based on the Pythagorean Theorem and requires the vector coordinates.

### Step 1

Square the coordinate "X" of the vector. For example, if the vector has coordinates (6,-8) then 6^2 = 36.

### Step 2

Square the coordinate "Y" of the vector. In this example, (-8)^2 = 64.

### Step 3

Add up squares of coordinates. In this example, the sum is 36 + 64 =100.

### Step 4

Take the square root of the sum to compute the magnitude of the vector. In this example, the magnitude is square root of 100 that is 10.